Noncommutative harmonic analysis

Classical Fourier Analysis

Published in Gregory S. Chirikjian, Alexander B. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis, 2021

Gregory S. Chirikjian, Alexander B. Kyatkin

In contrast to classical Fourier analysis, which is built on the arithmetic of scalar addition and multiplication (commutative operations), the more modern area of mathematics referred to as noncommutative harmonic analysis is unknown to the vast majority of engineers. In fact it is unknown to most scientists outside of theoretical physics.

Nonlinear nonhomogeneous Neumann problem on the Heisenberg group

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Journal Information

Published in Applicable Analysis, 2022

F. Sarafi, A. Razani

The Heisenberg group is an example of a sub-Riemannian manifold homeomorphic, but not bi-Lipschitz equivalent to the Euclidean space. The Heisenberg group (and more generally, stratified groups) is a special case of metric measure spaces with doubling measures. Its metric is derived from curves which are only allowed to move in so-called horizontal directions. The applications of the Heisenberg group include several complex variables, subelliptic equations and noncommutative harmonic analysis (see [1,2]).

Noncommutative harmonic analysis

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Classical Fourier Analysis

Nonlinear nonhomogeneous Neumann problem on the Heisenberg group